Answer

Verified

351.3k+ views

**Hint:**As we can see that there is a pattern of the numbers. Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. In this question we have to find that pattern that binds them all and then apply on them and then we find the next number on the basis of it.

**Complete step by step solution:**

We have been given a pattern here $41,12,163,94,365,256,\,\_\_\_\_$

We have to analyse the relation between these numbers. Since these are not any perfect squares or there is any addition of numbers between them.

Let us take the alternate series which means there are two series combined in one. The first one is $41,163,365$.

When we add $41 + 122$ we get $163$ and then when we add $163 + 202 = 365$. We should note that the difference between their differences is $80$.

Their differences are $202 - 122 = 80$.

In the second series we have $12,94,256$. Here again we can see that the difference between their differences is $80$ i.e. it can be written as $12( + 82) = 94( + 162) = 256$.

The differences are $162 - 82 = 80$.

So from the above we can write that the next pattern will be $365( + 282) = 647$.

**Hence the required next number is (A) $647$.**

**Note:**

In this kind of question we should always try to first find the pattern between the numbers. There are several patterns as there can be differences between the numbers as we can see in Arithmetic progression, there can be a perfect cube of the numbers. For example the series of numbers $8,27,64,125...$. These are the perfect cubes i.e. ${2^3},{3^3},{4^3},{5^3}$, so we can say that the next number in the pattern is ${6^3} = 216$.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Guru Purnima speech in English in 100 words class 7 english CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Select the word that is correctly spelled a Twelveth class 10 english CBSE